Dynamics Controls 2 PDR AAE 451 Team 2

Dynamics & Controls 2 PDR AAE 451: Team 2 Michael Caldwell Jeff Haddin Asif Hossain James Kobyra John Mc. Kinnis March 10, 2005 Kathleen Mondino Andrew Rodenbeck Jason Tang Joe Taylor Tyler Wilhelm 1

Overview n n n n n March 10, 2005 Aircraft 3 -View Trim Diagram Loop Closure Description Block Diagram Aircraft Transfer Function Pitch Rate Gyro Transfer Function Servo Transfer Function Gain Calculation Root Locus, Bode, and Nyquist Plot [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 2

Aircraft 3 -View Mission Requirements March 10, 2005 n 15 min. endurance n Take-off distance ≤ 60 ft. n Vstall ≤ 15 ft/s n Vloiter ≤ 25 ft/s n 35 ft. turn radius [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 3

Effect of Control Surface Deflection: Lift Roskam, Jan, Airplane Design Part. VI: Prelimenary Calculation of Aerodynamic, Thrust, and Power Characteristics, 2000 March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 4

Effect of Control Surface Deflection: Pitching Moment Roskam, Jan, Airplane Design Part. VI: Prelimenary Calculation of Aerodynamic, Thrust, and Power Characteristics, 2000 March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 5

Trim Diagram Trimmed Maximum CL CL Max (xref = xcg) α CL Max α = 0 o March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 6

Loop Closure Description n Pitch Rate feedback to the Elevator Objectives: 1) 2) March 10, 2005 Establish longitudinal stability by using pitch rate feedback by varying damping ratio of the short period mode from 0. 83 to 0. 99. Numerical values for all physical constants in the transfer functions. [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 7

Block Diagram Pilot Input March 10, 2005 Elevator Servo _ + He(s) Aircraft e(s) q(s)/ e(s) K H (s) Feedback Gain Pitch Rate Gyro [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] q(s) 8

Dynamic Models n March 10, 2005 Aircraft Transfer Function [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 9

Longitudinal Non-Dimensional Stability Derivatives Equation Description Pitching moment coefficient due to elevator deflection March 10, 2005 Value = -0. 029 Pitching moment coefficient due to angle of attack = -0. 008 Pitching moment coefficient due to rate of change of angle of attack = -0. 518 Pitching moment coefficient due to pitch rate = -0. 011 Lift coefficient due to elevator deflection = -11. 72 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 10

Longitudinal Dimensional Stability Derivatives Equation March 10, 2005 Description Value Pitch angular acceleration per unit elevator angle = -30. 04 [(rad/s 2)/rad] Vertical acceleration per unit elevator angle = -32. 39 [(ft/s 2)/rad] Pitch angular acceleration per unit angle of attack = -0. 007 [(rad/s 2)/rad] Pitch angular acceleration per unit rate of change of AOA = -9. 13 [(rad/s 2)/(rad/s)] Vertical acceleration per unit angle of attack = -243. 25 [(ft/s 2)/rad] Pitch angular acceleration per unit pitch rate = -8. 61 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] [(rad/s 2)/(rad/s)] 11

Dynamic Models n Aircraft Transfer Function (short Period Approx. ) n Aircraft Transfer Function (Flat Earth Predator) March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 12

Natural Frequency and Damping Ratio n Undamped Natural Frequency n Damping Ratio March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 13

Dynamic Models n Pitch Rate Gyro Transfer Function n Futaba GYA 350 Gyro : ¡ ¡ ¡ March 10, 2005 The Gyro Mixer The Gyroscope or Sensor The Switch/Gain Control Unit (SW Unit) [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 14

Dynamic Models n Servo Transfer Function n Hitec HS-55 Economy Sub Micro Servos The servo is used to convert voltage ( v) to elevator deflection ( e) n March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 15

Gain Calculation, k n First Trial: Determine k by trial and error: - Using the modified Design. Pitch. m file - Matlab code to approximate short period mode n Second Trial: - Flat Earth Predator - SISOTOOL k = 0. 0857 March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 16

Root Locus March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 17

Root Locus March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 18

Gain Calculation, k n For k = 0. 0857 March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 19

Bode Plot March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 20

Nyquist Plot March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 21

Questions ? March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 22

Appendix March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 23

Tail Sizing Comparison Class 1 Sizing Class 2 Sizing Canard Area Sht Vertical Tail Area Svt (each) March 10, 2005 1. 432 ft 2 1. 557 ft 2 0. 915 ft 2 0. 912 ft 2 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 24

Control Surface Sizing Span (ft) Chord (ft) Area (ft 2) March 10, 2005 Aileron 2. 62 0. 20 0. 524 Elevator 1. 92 0. 33 0. 634 Rudder (each) 0. 82 0. 50 0. 410 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 25

Control Surface Comparison Team 2 Spring 2005 Team 1 Fall 2004 Team 4 Fall 2004 Aileron Area Wing Area 0. 100 0. 204 . 0102 Elevator Area Canard Area 0. 442 0. 198 0. 258 Rudder Area Vtail Area 0. 448 0. 400 0. 326 *Areas compared – Ongoing Research for Moments March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 26

Actual Static Margin n March 10, 2005 Xcg = 1. 70 ft Xnp = 1. 85 ft Static Margin = 14. 80% [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 27

Variation of Yawing Moment Coefficient with Sideslip Angle Roskam, Jan, Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes, 1977 March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 28

Variation of Rolling Moment Coefficient with Sideslip Angle Roskam, Jan, Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes, 1977 March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 29

Variation of Pitching Moment Coefficient with Elevator Angle Roskam, Jan, Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes, 1977 March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 30

Variation of Yawing Moment Coefficient with Rudder Deflection Roskam, Jan, Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes, 1977 March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 31

Variation of Rolling Moment Coefficient with Aileron Deflection Roskam, Jan, Methods for Estimating Stability and Control Derivatives of Conventional Subsonic Airplanes, 1977 March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 32

Longitudinal Static Stability Aircraft starting from straight, level, trimmed flight with small perturbations has two independent natural motions acting about an aircraft’s pitch axis. Longitudinal Modes: 1. 2. March 10, 2005 Short Period Mode (Heavy damping and high frequency) Phugoid Mode (Less damping and low frequency) [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 33

Longitudinal Static Stability n March 10, 2005 Short Period Mode: [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 34

Longitudinal Static Stability n March 10, 2005 Phugoid Mode: [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 35

Longitudinal Static Stability n Short Period Mode n Phugoid Mode March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 36

Lateral Directional Stability Lateral directional EOMs can be expressed by a second order differential equation and two first order differential equations. Lateral-directional Modes: 1. 2. 3. March 10, 2005 Dutch Roll Mode Spiral Mode Roll Mode [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 37

Lateral Directional Stability n March 10, 2005 Dutch Roll mode: [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 38

Lateral Directional Stability n Dutch Roll mode: n Spiral Mode: n Roll Mode: March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 39

Lateral Directional Stability n Desired spiral mode time constant is excess of 20 seconds n Desired roll mode time constant is 0. 5 to 3 seconds March 10, 2005 [ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 ] 40